DOM... get the green card and apply..... no need applying without it....as all the applications will ask if your CURRENTLY have the right to work in the US....
Figuring you have to live in the states to get the green card... you are probably going to have to work at a regional or ACMI cargo carrier that will hire you almost immediately while you are applying and waiting for a call from a Legacy/major carrier. Thats the way I see it... ymmv